Exam (elaborations)
A LEVEL MATHS QUESTIONS AND ANSWERS WITH SOLUTIONS 2024
- Course
- Institution
A LEVEL MATHS QUESTIONS AND ANSWERS WITH SOLUTIONS 2024
[Show more]
Content preview
A LEVEL MATHS QUESTIONS ANDANSWERS WITH SOLUTIONS 2024
if two lines are perpendicular, what must their gradients equal to when multiplied together? - ANSWER -
1
What is the equation to calculate the gradient of a line? - ANSWER y₂-y₁/x₂-x₁
What is the equation to calculate the length of a line? - ANSWER √(y₂−y₁)^2 + (x₂-x₁)^2
What is the equation to calculate the midpoint of a line? - ANSWER (x₂+x₁) over 2 , (y₂+y₁) over 2
What is the equation of a circle? - ANSWER x²+y²=r²
How do you find the midpoint of a circle from the equation? - ANSWER (x-a)²+(y-b)²=r²
If a factor of a line equation is (x-2)², or the line equation is just y=(x-2)², how many solutions does (x-2)²
give and what does this look like on a graph. - ANSWER This gives just one solution, that x=2. This means
that the line just touches the x axis at (2,0).
What does a x⁴ and a -x⁴ graph look like? - ANSWER An x⁴ looks like a W
A -x⁴ looks like an upside down W
What does an x³ and a -x³ graph look like? - ANSWER An x³ graph appears to travel from bottom left to
top right with two curves
A -x³ graph appears to travel from bottom right to top left with also two curves
How do you find the min/max point of a quadratic? - ANSWER Complete the square; the x in the bracket
will be the x coordinate and the number out the bracket will be the y coordinate
How do you establish that (x-3) for example, is a factor of an equation? - ANSWER Sub in 3 for example.
If it is a factor, there will be no remainder and it will equal 0.
, If no factors of an equation are given and you are asked to factorise, what should you do? - ANSWER Try
small integers using substitution
How do you quickly find a remainder of an equation given a factor? - ANSWER Substitute in the factor,
and this will equal the remainder
What change does the a in f(x) + a cause to a graph? - ANSWER It causes the graph to move in the
direction of the y axis
What change does the a in f(x+a) cause to a graph? - ANSWER It causes the graph to move in the
direction of the x axis
How do you change the factors of a graph that has been translated by f(x+a)? - ANSWER If it was
translated by moving to the right by 3, you would add 3 to each factor bracket. e.g (x+3) would change to
(x+6)
What can pascals triangle be used for during binomial expansion? - ANSWER Pascals triangle shows the
coefficients of the expansion.
It also shows a pattern of the a²,a³ b²,b³ etc.
What is the pattern of the a² etc and b² etc? - ANSWER The a's decrease as you go across the triangle.
The b's increase as you go across the triangle
How else can you find a coefficient of an expansion? - ANSWER Using ⁿCr
What does the n and r stand for in nCr? - ANSWER n is the number it is to the power of. r is the number
of term which you want to find
What does r start at? - ANSWER It starts from 0 and then progresses
What is nC0 always equal to no matter what n is? - ANSWER 1
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Performance. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $15.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
77254 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now